Talk given by Joshua Vogelstein, of Johns Hopkins University to the Redwood Center for Theoretical Neuroscience at UC Berkeley on August 13, 2008.
Great technological and experimental advances have recently facilitated the imaging neural activity both in vivo and in vitro using calcium sensitive fluorescence observations. We present here complementary analytical tools maximizing the utility of these data sets. First, we describe a fast method, that can simultaneously infer spike trains from a population of neurons in real time on a typical single processor computer. More precisely, we apply an approach called basis pursuit (or non-negative convex optimization with a log-barrier penalty term), and use an additional trick (tridiagonal matrix inversion) which capitalizes on the exponential nature of the calcium filter, to infer spike times both more accurately and faster than the optimal linear (i.e., Wiener) filter. Second, we describe a sequential Monte Carlo (SMC) expectation maximization algorithm that generalizes many of the assumptions made to derive the fast method. The SMC approach (often called particle filtering) approximates the distribution of the hidden variables (calcium and spikes) by recursively generating weighted samples, which it uses to form a histogram that approximates the actual distribution. By integrating over this histogram, instead of the true distribution, we construct a very accurate approximation. Using such an approach enables us to (i) incorporate errorbars on the estimate, (ii) allow for saturation of the fluorescence signal, and (iii) consider spike history effects such as adaptation, facilitation, and refractoriness. While slower, this strategy still works in real time for each observable neuron. We show how both methods can condition the inferred spike trains on external stimuli, and achieve superresolution, i.e., infer not just whether a spike occurred within a stimulus frame, but when within that frame. Furthermore, both methods have a relatively small number of parameters, and each of the parameters may be estimated using standard gradient ascent techniques, without needing additional calibration experiments or ratiometric dyes. We demonstrate the advantages of each of these approaches over the Wiener filter using data sets recorded using both epifluorescence and 2-photon imaging.